The Eagles had been victorious in their last three meetings with the Clarets, including a 3-1 win at this venue back in March.
They got off to a fine start towards the half-time break courtesy of Wilfried Zaha, who buried the ball in from a tight angle on the left after receiving a long ball from centre-back Scott Dann.
2 - Wilfried Zaha has now scored in back-to-back Premier League games, having gone 13 without a goal in the competition. Revived. #BURCRY— OptaJoe (@OptaJoe) November 30, 2019
The Ivory Coast international was on target against Liverpool last week for the first time this season. He now has consecutive Premier League goals after going 13 matches without finding the back of the net.
Jeffrey Schlupp came on for Andros Townsend in the 70th minute and made it 2-0 for Palace with a lovely strike after Burnley defender Ben Mee made a mess of the ball.
It was the Ghanaian full-back’s first goal in 21 league games, stretching back to a tie with Fulham in February.
The South London club will host Bournemouth next at Selhurst Park on Tuesday.